Polynomial Arithmetic

Explore like-term addition, distribution and products, special products.

Lesson 1 of 53 parts Practice Flashcards

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Like-Term Addition

Objective: Explain like-term addition and use it to solve or interpret a problem.

Add or subtract polynomial terms only when their variable powers match; keep other powers separate and use descending-power order when useful. No, their variable parts differ.

Worked examples

Try itPolynomial Arithmetic — practice 1.1: Find the x² coefficient in (4x²+5x)+(5x²+1).Show answer

Step 1: Identify like x² terms: 4x² and 5x². Step 2: Add coefficients 4+5. Step 3: The coefficient is 9.

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Like-Term Addition

Objective: Explain like-term addition and use it to solve or interpret a problem.

Add or subtract polynomial terms only when their variable powers match; keep other powers separate and use descending-power order when useful. No, their variable parts differ.

Worked examples

Try itPolynomial Arithmetic — practice 1.1: Find the x² coefficient in (4x²+5x)+(5x²+1).Show answer

Step 1: Identify like x² terms: 4x² and 5x². Step 2: Add coefficients 4+5. Step 3: The coefficient is 9.

Distribution and Products

Objective: Explain distribution and products and use it to solve or interpret a problem.

Multiply each term in one polynomial by each term in the other; apply exponent rules and combine like terms. An area grid can organize partial products. They represent the same variable power.

Worked examples

Try itPolynomial Arithmetic — practice 2.1: Find the x coefficient of (x+2)(x+8).Show answer

Step 1: Expand: x²+8x+2x+16. Step 2: Combine the two x terms. Step 3: The coefficient is 10.

Special Products

Objective: Explain special products and use it to solve or interpret a problem.

The identities (u+v)²=u²+2uv+v² and (u+v)(u−v)=u²−v² are consequences of distribution, not extra order rules. There are two uv cross-products.

Worked examples

Try itPolynomial Arithmetic — practice 3.1: Find the x coefficient of (x+3)².Show answer

Step 1: Expand (x+3)(x+3). Step 2: The cross terms are 3x and 3x. Step 3: The coefficient is 6.

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